我們主要是研究下列型態的差分方程式，其中{c_(n)}是已知序列。設法找出解的充要條件。a_(n)=a_(n+1)-c_(n){[a_(n+1)]^2+α^2}For sequence{c_(n)},we consider the following difference equation.a_(n)=a_(n+1)-c_(n){[a_(n+1)]^2+α^2} We will apply the method of backward induction to establish the existence and the uniqueness under certain conditions.